Math Stats & Data Mining

I have been in college for 14 years. I tell my kids that puts me in 26th grade. In that time I have taken a ton of math and statistics courses and in all of them similar approaches to homework were used. It goes like this…

Learn the material then do the homework.

I took a class on Geometry teaching methods last semester and a whole new world was opened to me.

Everyone knows that every student comes into the classroom with prior knowledge from different areas of their lives. Many people will also agree that effective instruction includes making connections to this prior knowledge. In order to make these connections in the traditional approach we usually try to choose homework problems in the major or content area of the student’s studies. I think the majority opinion about math and statistics of my students when they enter my classroom is some proof that this isn’t working. If we were making connections with students effectively I believe that the attitude about the subject(s) would be much better.

So, what was shown to me in the class I took was, if you put the problems first and let the students work themselves through the process using the “regular” knowledge they have coming in you will make a much more secure connection with the previous knowledge that they have. For example, the first lecture in my statistics course is on how to organize and summarize data. In the past I have just started in assuming that, since much of the information is common sense, the students will not have trouble. Then I am always surprised when, and I think it’s because it is a scary statistics class, the students don’t seem to get it very easily.

So, this summer I am trying out the backwards approach. On the first day of class I had the students get into groups and I handed out data sets, both qualitative and quantitative. Before showing them anything I gave them the task of organizing and summarizing the data. It was amazing! Every group in both of my classes started out down the path that I was going to show them, all on their own. After a whole-class discussion we moved on to the slides. These students are just turning in their first exam but I had NO questions on this part of the material and that is a first for me in 6 years of teaching.

I have used a similar approach for introducing probability and it also went well. I am now going to look at all of my classes and see what I can do to incorporate this method and see how it goes. I really do think I’ve been turned on to a wonderful shift in thinking. I’ll keep you posted!

In this semester of my PhD education I am taking a course on Project Based Learning (PBL). The major outcome of this class is that I will design a PBL unit. I know that I would like to do this unit on linear regression but I still need help.

I would like to be able to use the project outcomes to help a business, school, or community. The students will be creating a (hopefully) accurate linear regression equation that can be used for prediction. I am looking for ideas of variables that are believed to be associated (e.g. height and weight) that can be researched data can be collected and an analysis can be done.

I have the option of having the students work in groups which means that I could have them each look at a different relationship. The other option would be to have the whole class work on the same relationship and work individually.

No idea is a bad one so please feel free to reply with any brainstorm that may arise.

Thanks ahead of time!

I have been completely immersed in the world of statistics for the last three and a half years. I have had the privaledge of teaching for most of that time as well. What I am amazed to see over and over again is that there are hundreds of people out there who are afraid of statistics and don’t know why!

My first question when someone says, “I hate statistics,” is always, “Why?”

The most common answers I get are:

“I am really bad at math.”
“My friend said it was hard, and I have to take it.”
“I hated that class.”

My response to the first one is that statistics uses some basic math but really its the art of understanding information.

To the second I usually say nothing because no one can get through college on what other people do in their classes.

The third is the one that interests me the most because usually a bad instructor was to blame. I don’t ever want to be one of those. Now, you have to know that the reason that I ask why is because as an eductator I want to know things that I can do to improve my students’ experience with statistics.

What I need is the nitty gritty. Why didn’t/don’t you like your statistics class? Is it because the examples didn’t apply to you? Is it because the instructor couldn’t answer your questions? Is it because it was all words and not enough graphics? Is it because you had a bad attitude going into it so the class never stood a chance in your mind? I am looking for people’s specific comments on the question, “Why is statistics so scary?”

We have a relatively new “virtual” department at Iowa State University (ISU) called Human Computer Interaction (HCI). What I mean by virtual department is, that in order to get a degree in HCI you must co-major in it and first have a home department. Also, most of the HCI faculty also have home departments somewhere else.

According to Wikipedia, HCI is, “is the study of interaction between people (users) and computers. It is an interdisciplinary subject, relating computer science with many other fields of study and research.”

This is similar to how the field was described to me, with concrete examples of how the fields of psychology and sociology have real issues with trying to make usable software for students in their fields. So, I assumed that this was an accurate description of HCI departments across the board. I had no idea that it so much more complex than that. I was first introduced to it by my advisor in the statistics department who is an HCI faculty member.

I was immediately interested in the field because there is a ton of statistics that goes into determining how successful the programs are, as well as the statistics that are incorporated into research in any field. One of the reason I like statistics so much is that it is applicable to any subject. Having unending interests in many different fields this appealed to me greatly. I soon decided that no matter what I got my PhD in, HCI would be part of it.

That was when I started asking around (I had many friends who were computer science majors). I soon found out that depending on who you asked, ISU either had a great or a horrible HCI department. This confused me because I was under the assumption, as I stated before, that the definition of HCI was the same across the board. After that I did a little asking around and searching on the internet and came up with a little more clarifying information.

At ISU we have a world renowned virtual reality lab (VRAC) and that is the driving force behind our HCI department. A

Below are a few descriptions and bits of information on this field that I was able to find from a couple different institutions, with a little help from Google, of course…

Carnegie Mellon has a Human-Computer Interaction Institute and their mission is:
“To create effective, usable, enjoyable experiences with technology through interdisciplinary research in engineering, design, computer science, and the behavioral and social sciences, and to understand the impact of technology on individuals, groups, and organizations.” ( http://www.hcii.cmu.edu/ ) They also have a video at their site that explains their program.

Stanford University has a neat site with many different publications (.pdf files) about new technologies and techniques in the field. (http://hci.stanford.edu/ ) I read two neat articles about prototyping camera-based interaction through examples, and also one discussing gaze-enhanced scrolling techniques. The first articles describes a new software called Eyepatch, described in the article as a tool that, “allows novice programmers to extract useful data from live video and stream that data to other rapid prototyping tools, such as Adobe Flash, d.tools [14], and Microsoft Visual Basic.” The other article investigates ways to scroll by observing the gaze of the user. I found that information fascinating.

The University of Maryland has a HCI Lab (HCIL) and they describe their work, “The HCIL is an interdisciplinary lab comprised of faculty and students from Information Studies, Computer Science, Education, English, Business, and Psychology. Our current work includes new approaches to information visualization, interfaces for digital libraries, multimedia resources for learning communities, zoomable user interfaces (ZUIs), technology design methods with and for children, mobile and pen-based computing and instruments for evaluating user interface technologies.” (http://www.cs.umd.edu/hcil/about/ )

This summer North Carolina State University ran a really neat workshop that involved mathematical and statistics modeling. I am always interested in how people are advancing students in applied math and statistics. The website (see below) for the workshop describes the objective as,

“The objective of the workshop is to expose graduate students in mathematics, engineering, and statistics to challenging and exciting real-world problems arising in industrial and government laboratory research. The students also learn about the team approach to problem solving.”

Real-world problems and a team approach to problem solving are the important things listed in my opinion. There is not enough interest in our fields and I personally believe that is because there aren’t enough people trying to recruit people into the subjects. One way thing that I believe is an integral tool in building interest is showing how the fields of math and statistics apply to the real world. That is one of the main reasons that I fell in love with mathematics as an undergraduate. While some people are born math lovers some of the rest of us have to be converted. My hat’s off to workshops like this one at NC State that highlight the applications of mathematics and statistics in the real world.

The procedure of the workshop was to team up students with the scientists and engineers that deal with the real world problems in their work. The problems that were given to them were to make some advancement in the field in which they worked. There were a couple mentors for each group.

I was also impressed that they didn’t require any experience to apply, just commitment. I like it when programs are open to anyone who may want to try out a little math or stats in the real world.

To read for yourself about the workshop visit the webpage at http://www.ncsu.edu/crsc/imsm/index.php

If I have a craving for Granny’s (my husband’s grandma) ham balls I wouldn’t dare even make my shopping list without first consulting the recipe card that was handed down to me some time after my husband and I got married. The same goes for a couple of other hallowed recipes that calm my husband in times of anxiety.

I was thinking the other day about how much like recipes formulas are. So much alike, in fact, that I would say that recipe could be a synonym for formula. And yet, it seems that the formula sheet is the last place that my students turn for help instead of the first.

When one is doing any statistics there are formulas close at hand. I urge you to turn first to the formulas before throwing your hands up in the air and pronouncing that statistics is for the birds. The type of variables that you are describing or comparing will decide what type of analysis needs to be done and from there the formulas follow closely. (e.g. linear regression analysis, categorical data analysis, etc.) So, let the words of the problem lead you to the correct formula to use for your data analysis.

The only other major difficulty that I see in the classroom is a fear of multiple variables in an equation or formula. This is an Algebra problem and another topic for another day.

Part of my interests are pathway difficulties. These are roughly paraphrased as the obstacles that students come up against (be it for any number of reasons) that keep them from moving from one concept to another. I plan to use recipes in my lectures about using the formula sheet from now on. I will report back on any feedback that I get from students.

Spending three years submerged in graduate level statistics tends to cloud judgment of the knowledge that the lay man should have on that subject. Since my education in this subject is drawing to a close I am looking to what lay ahead. It is time to answer the question that I have been asked for years: “What do you do with a Master’s in statistics?”

Trying my hand at writing an eBook is one thing I have settled on. In order to get a smart start I wanted to research what things people wanted to learn about statistics. I used some of the research skills I have developed and the wonderful world wide web to get some surprising information. My searches revealed that a hot topic of interest is one of the most basic ideas of my field, histograms and bar charts. These are the most basic tools in statistics because they are the graphics most commonly used to describe single variable data sets. Almost every business setting in existence has some setting in which a list could be displayed.

In my corporate world experience there were many occasions when the performance of a certain department or sales unit was recorded over a certain amount of time and when those numbers were presented they were still either in a list or just the minimum and maximum values were presented. Knowing what I do now I wonder if anyone in the office had ever had to make a histogram or if they had any idea how easy it was to do. Graphically representing data in a chart is easy on the eyes and the brain. Our minds naturally take in charts and we can mentally input so much more information than with a list of numbers.

So, for those who have never been exposed to the world of statistics or those who took a class so long ago that they have cobwebs on that information look forward to my upcoming eBook. The title of the first draft is: A Step by Step Guide to Meaningful Histograms and Bar Charts.

If there are any other concepts that you would like to see addressed here feel free to let me know and if I don’t already know about it I will research and learn!!